Derive ideal gas equation from diff.laws

 

Asked by gurjeetsandhu0335 | 20th Dec, 2018, 06:46: PM

Expert Answer:

The gas equation is an equation used in chemical equations for calculating the changes in the volume of gases when pressure and temperature both undergo a change,

thereby giving a simultaneous effect of changes of temperature and pressure on the volume of a given mass of dry gas.

According to Boyle's law:             

 

straight V proportional to 1 over straight P space space space space space space space at space contsnt space straight T space space...... open parentheses 1 close parentheses  

According to Charles' law:       

         

straight V proportional to straight T space space space space at space contant space straight P space.... open parentheses 2 close parentheses 

According to Avogadro's law:  

 

straight V proportional to straight n space space at space constant space straight T space and space straight P space space..... open parentheses 3 close parentheses   

where n is the number of molecules

 straight V proportional to 1 over straight P cross times straight T cross times straight n

straight V equals straight R cross times 1 over straight P cross times straight T cross times straight n

PV equals space nRT

 

where, R is molar gas constant.

 

If the volume of a given mass of a gas changes from V1 to V2, its pressure changes from P1 to P2 and its temperature changes from T1 to T2, then

 fraction numerator straight P subscript 1 straight V subscript 1 over denominator straight T subscript 1 end fraction equals fraction numerator straight P subscript 2 straight V subscript 2 over denominator straight T subscript 2 end fraction

The above equation is called the gas equation. This equation is also called the combined gas equation.

 



Answered by Varsha | 21st Dec, 2018, 12:04: PM